Spring 2010 Algebraic Number Theory

Mathematics G4657 section 001

Last updated on Apr. 1, 2010.

Course Schedule
Time: Tuesday 2:30 pm–4:00 pm, Thursday 2:30 pm–3:30 pm
Location: Room 622, Mathematics Building
Name: Weizhe Zheng
Office: Room 606, Mathematics Building; Phone: 212-854-3003
Email: zheng at math dot columbia dot edu
Office hours: Tuesday and Thursday 10 am–11 am, in instructor's office
References (incomplete list)
Algebraic Number Theory, edited by J. W. S. Cassels, A. Fröhlich, Academic Press, 1967.
Algebraic Number Theory, by S. Lang, 2nd ed., Springer-Verlag, 1994.
Algebraic Number Theory, by J. Neukirch, Springer-Verlag, 1999.
Galois theory, commutative algebra
Lecture Notes
Abridged notes with no proofs. Updated on Feb. 15, 2010.
This syllabus is subject to change.
Date Topic
Jan. 26 global fields
Jan. 28 places
Feb. 2 completion
Feb. 4 extension of places
Feb. 9
Feb. 11 Dedekind domains
Feb. 16
Feb. 18 differents and discriminants
Feb. 23 local fields
Feb. 25 adeles
Mar. 2 ideles
Mar. 4
Mar. 9 Pontryagin duality
Mar. 11 duality for local fields
Mar. 23 local zeta functions
Mar. 25 duality for adeles
Mar. 30 global zeta functions
Apr. 1 Kummer theory
Apr. 6 local class field theory: statements
Apr. 8 global class field theory: statements
Apr. 13 the first inequality
Apr. 15 Chebotarev's density theorem
Apr. 20 the second inequality
Apr. 22 Artin reciprocity
Apr. 27 global existence theorem
Apr. 29 local class field theory
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